1. Field of the Invention
The present invention relates to a recording medium on which a program for generating mask data is recorded, a method for manufacturing a mask, and an exposure method.
2. Description of the Related Art
Exposure apparatuses are used in processes for manufacturing integrated circuits (ICs), large scale integrated circuits (LSIs), and other semiconductor devices. Exposure apparatuses illuminate a mask (reticle) with an illumination device, and project an image of a pattern drawn on the mask onto a substrate (wafer) using a projection optical system for substrate exposure.
Among techniques for improving the resolution performance of an exposure apparatus is super-resolution technology. According to the technology, for example, an auxiliary pattern that itself resolves no image is formed on a mask. Such a mask is then used to resolve a pattern to be formed on a substrate. Methods available for designing the layout of an auxiliary pattern include one using an interference map (Robert Socha, et al., “Simultaneous Source Mask Optimization (SMO),” Proc. SPIE 5853, 180-193 (2005)), one using inverse lithography (Daniel S. Abrams, et al., “Fast Inverse Lithography Technology,” Proc. SPIE 6154, 61541) (2006)), and one discussed in Japanese Patent Application Laid-Open No. 2009-093138.
According to Robert Socha, et al., “Simultaneous Source Mask Optimization (SMO),” Proc. SPIE 5853, 180-193 (2005), the shape of a main pattern to be transferred to a substrate and the shape of an auxiliary pattern are separately determined in the pattern shape optimization. Since both the shapes can affect the projection image projected on the substrate, the separately-determining method tends to be trapped in a local minimum (local solution) and is less likely to reach an optimum shape (optimum solution) of the mask pattern. There has also been an issue that the amount of calculations needed to determine an optimum solution increases.
The method discussed in Japanese Patent Application Laid-Open No. 2009-093138 determines a mask pattern by deforming a main pattern and an auxiliary pattern. The method uses an approximate aerial image, not a strict image that is calculated based faithfully on physical models. Since the mask pattern is determined based only on its approximate aerial image, there is a possibility of causing errors in the result of optimization. Approximate aerial images may exhibit a complicated pattern, which can complicate the mask pattern in shape.
The inverse lithograph discussed in Daniel S. Abrams, et al., “Fast Inverse Lithography Technology,” Proc. SPIE 6154, 61541J (2006), determines a main pattern and an auxiliary pattern at a time. The inverse lithography, however, has the drawbacks that the resulting mask pattern is complicated since the mask pattern is generated from a two-dimensional map that has a complicated pattern of continuous intensities. Hence the mask manufacturing cost is high.